Q-Stem(Rephrased)


We are asked is 1/2 *CB * AC = 1/2 * AD * AB or IS CB X AC = AD X AB  ?

St(1) :- AC X AC = 2 (AD X AD)
It doesn't tell us anything about CB and AB that are necessary to answer the question stem. Insufficient

St (2) :- ABC is isosceles
Let the side AC =x units => BC =x units too and ABC is a 45-45-90 triangle.
AB = sqrt(2)x but we have no information about AD. (Insufficient)

Combining both,

AC=BC=x units and AB = sqrt(2) x 
=>Area of ABC = 1/2 * x*x 
= x^2/2

From St(1), AD = Sqrt(AC^2/2)  = Sqrt (x^2/2)

ABC area = 1/2 *x*x =x^2/2

ABD area = 1/2  * AB * AD 

= 1/2 * √2 x *  √(x^2)/2

= ½ * √2 x *  x/√2  
= x^2/2
Thus area of ABC =area ABD (Sufficient)
(option c)